Integrated approach to modeling and control of flexible structures via ℓ∞ loopshaping

An integrated approach is proposed to modeling and control of lightly damped systems such as flexible structures using frequency loopshaping in ℓ∞. Normalized coprime factors of the shaped plant model are identified with quantification of the modeling error in ℓ∞ norm. Feedback controllers are synthesized to stabilize the true but unknown plant albeit the nominal feedback system, consisting of the identified model and the feedback controller, may not be stable. A complete design procedure is presented that integrates modeling and control in frequency domain. It is shown that as the ℓ∞ norm of the modeling error measured in normalized coprime factors of the system is reduced, the existence of stabilizing feedback controllers for the true unknown plant is ensured